Parent

Reference Book

Written by the

iDRAGONS

2

Parent Reference BookWelcome to the Parent Reference Book! This book is for those

parents and other adults that are new to their kid’s math algorithms. If you’re one of those parents, then this book is right for you.

This book is similar to the Student Reference Book, but it only has the new math algorithms that most parents have trouble on.

Table of ContentsCounting Up Method Subtraction 2-4

Left to Right Subtraction 5-6

Array Multiplication 7

Lattice Multiplication 8-10

Partial Products Multiplication 11-12

Partial Quotients Division 13-15

Answers to Practice Problems 16-21

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Counting Up Method (Subtraction)

The counting up method of subtraction is similar to the process of making change. You count up from the lesser number to the greater number to find the difference.

EXAMPLE: 425-48

Step 1: Take the smaller number. In this problem, it’s 48. Count up to the nearest ten. In this case you would need 2 to count up to the nearest ten which is 50. Step 2: Count up to the nearest 100. In this case you would need 50 to count up to 100.

Step 3: Count up to the highest hundred needed. In this case to count up to 400 you would need 300.

Step 4: See what else you need to count up to the number you are trying to reach. In this problem it’s 25.

4

Step 5: To get the solution, add up all of the numbers that you added while counting up. 2 + 50 + 300 + 25= 377

48+250

+ 50 100 + 300 400

+ 25 425

Now try a practice one.

367 - 25

Once you think you have it, turn to page 16 and check your work.

5

Left to Right SubtractionLeft to right subtraction begins on the left and works to the right one place value at a time. It can be used for subtracting any subtraction problems with 2 or more digits.

EXAMPLE: 450-264Step 1: Subtract the hundreds. 450

-200250

Step 2: Subtract the tens. 450 -200

250 -60

90

Step 3: Subtract the ones. 450 -200

250 -60

190 - 4

186

6

Now try a practice one.

613 - 215

Once you think you have it, turn to page 17 and check your work.

7

Array (Multiplication)

Arrays can be used to work show a multiplication problem.

EXAMPLE: 3 X 4

Step 1: Draw or arrange 3 rows of 4 objects.

Step 2: Count how many objects in all. That is your answer.

12

Now try a practice one. 5 X 2

Once you think you have it, turn to page 18 and check your work.

8

Lattice Multiplication

Lattice Multiplication is a type of math used to solve large number multiplication using a grid. Here are the steps.

EXAMPLE: 325 X 46

Step 1: Make the grid. Draw a grid that has as many rows and columns as the multiplicand and the multiplier. The grid shown here is for multiplying a 3-digit number by a 2-digit number. Draw a diagonal line through each box from upper right hand corner to lower left hand corner. Extend the lines beyond the grid.

Step 2: Write one number of the problem across the top and the other down the right side, lining up the digits with the boxes.

9

3 2 5

4

6

1 1

12

08

20

023

8

1 1

12

08

20

023

8

Step 3: Start multiplying. The multiplication is performed by multiplying the digits at the head of each row and column. Fill in each square of the grid with the product of the digits above and to its right, recording the products so that the tens are in the upper (diagonal) half of the square and the ones are in the lower half. If the product does not have a tens digit, record a zero in that triangle.

In the example shown here, the highlighted row and column give us 2×4=8, so we write 0 in the upper half of the square and 8 in the lower half.

Step 4: Add. Now add the numbers in the grid along the diagonals, starting from the lower right corner. Carry any tens into the top of the next diagonal.

In this example, the highlighted diagonal gives us 8+1+8+2=19, so we write 9 at the

10

3 2 5

3 2 5

4

6

4

6

1

1

49 5 0

bottom of the diagonal and carry the 1 to the top of the next diagonal to the left.

Step 5: To find the answer, read the digits starting down the left of the grid and continuing across the bottom. Here, the answer to 325 X 46 is 14,950.

Now try a practice one.

398 X 14

Once you think you have it, turn to page 19 and check your work.

11

Partial Products Multiplication

EXAMPLE: 67 X 53

Partial Products Multiplication is a way to multiply in which each number in a factor is multiplied by the other digits in the other factor. Here are the steps.

Step 1: Line up the numbers. 67X 53

Step 2: Multiply the ones by the ones. 7 X 3 = 21

Step 3: Multiply the tens (of the first number) by the ones (of the second number).

60 X 3 = 180

Step 4: Multiply the ones (of the first number) by the tens (of the second number).

7 X 50 = 350

Step 5: Multiply the tens by the tens.

12

60 X 50 = 3,000

Step 6: Add each of the products from the above steps.

3,000 350 180

+ 21

3,551

Now try a practice one.

28 X 51

Once you think you have it, turn to page 20 and check your work.

13

Partial Quotient Division

At each step in partial quotient division you find a partial answer. Then you find the product of the partial quotient and divisor and subtract it from the dividend. Lastly you add all the partial quotients to find the final quotient.

EXAMPLE: 1010 ÷ 6

Step 1: How many sixes are in 1010? Make your guess and write it to the right.

6 1010 100

Step 2: Multiply the divisor by the number you guessed. (In this example 6X100)

Step 3: Write this below the dividend. Subtract.6 1010 100 -600

410

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Step 4: How many sixes are in 410. Make your guess and write it to the right.

6 1010 100 -600 50

410

Step 3: Multiply the divisor by the number you guessed. (In this example 6x50)

Step 6: Write this below the dividend and subtract. 6 1010 100

-600 50410

-300110

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Step 7: Continue until the divisor will no longer go into the number you have left. If there is not a 0 then this is your remainder

6 1010 100 -600 50

410 10 -300 8

110 -60 50 -48 2

Step 8: Add the numbers on the right.

100 + 50 + 10 + 8 = 168 Answer: 168 R2

Now try a practice one. 936 ÷5

Once you think you have it, turn to page 21 and check your work.

ANSWERS TO PRACTICE PROBLEMS

16

Counting Up Method (Subtraction)

367-25

25+530

+ 70 100 + 200 300

+ 67 367

5 + 70 + 200 + 67 = 342

367-25=342

17

Left to Right Subtraction

613-215

613 -200

413

613 -200

413 -10

403

613 -200

413 -10

403 - 5

398

18

Array Multiplication

5 X 2

5 X 2 = 10

19

Lattice Multiplication

398 X 14

3 9 8

1

4

5 7 2

20

0 3

0 1 9

0 1 8

1 2

3 6

3 25

Partial Products Multiplication

28 X 51

28 51

8 1=8

20 1=20

8 50=400

20 50=1,000

1000

400

20

8

1,428

21

Partial Quotient Division

936 ÷ 5

187

5 936 100 -500 50 3436 20 -250 15 186 2 -100 86 -75 11 -10 1

22